Question: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$6.50$, and bags of cookies cost $$4.00$, and sales equaled $$47.50$ in total. There were $4$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Answer: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6.5x+4y = 47.5}$ ${y = x+4}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+4}$ for $y$ in the first equation. ${6.5x + 4}{(x+4)}{= 47.5}$ Simplify and solve for $x$ $ 6.5x+4x + 16 = 47.5 $ $ 10.5x+16 = 47.5 $ $ 10.5x = 31.5 $ $ x = \dfrac{31.5}{10.5} $ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $ {y = x+4}$ to find $y$ ${y = }{(3)}{ + 4}$ ${y = 7}$ You can also plug ${x = 3}$ into $ {6.5x+4y = 47.5}$ and get the same answer for $y$ ${6.5}{(3)}{ + 4y = 47.5}$ ${y = 7}$ $3$ bags of candy and $7$ bags of cookies were sold.